Let L=1−z2D2−2zD, D=d-dz and fz=∑n=0∞cnpnz, with Pn being the nth Legendre polynomialand f analytic in an ellipse with foci ±1. Set Lk=LLk−1, k≥2. Then the number of zeros of Lkfz in this ellipse is Oklnk.